# Weight Half Forms

Modular forms of weight $1/2$ are constructed directly as $q$-expansions following the explicit description given by Serre and Stark (see [[Serre and Stark, 1977](../../references.md#cite-serrestark)]).

## `WeightOneHalfData(M): ModFrm -> List`

For a space $M$ of modular forms of weight $1/2$, this returns the basis of the space as described by Serre and Stark. A list of tuples is returned; each tuple contains a character $\psi$ and an integer $t$, and the corresponding modular form is the theta series defined as the sum over all integers $n$ of $\psi(n) q^{(t n^2)}$.